along with a number of other compatibility conditions, see, e.g., [1]}. Let \(p\)  be a point in \(G_0\) , considered as a morphism \(p\colon A(G_0)\xrightarrow{}\mathbb {R}\) . Then one can form the map \((1\otimes p)\circ \varphi \colon B(Y)\xrightarrow{}B(Y)\) . For obvious reasons, we refer to such compositions with \(p\)  as evaluations. Running over all points \(p\) , we get a representation of the \(G_0\)  on \(B(Y)\) . This agrees with the coaction representation \(\pi \)  from above. The evaluated action of the bosonic group \(G_0\)  and the infinitesimal action of the conformal Lie superalgebra fit together to form a representation of the Lie–Hopf algebra \(A(G_0)^\ast \)  on \(B(Y) = \mathcal {M}\) .
